Cambridge International Mathematics

2 Illustrate on a 2 -dimensional grid the sample space for:

a rolling a die and tossing a coin simultaneously

b rolling two dice

c rolling a die and spinning a spinner with sides A, B, C, D

d twirling two square spinners: one labelled A, B, C, D and the other 1 , 2 , 3 , 4.

3 Illustrate on a tree diagram the sample space for:

a tossing a 5 -cent and 10 -cent coin simultaneously

b tossing a coin and twirling an equilateral triangular spinner labelled A, B and C

c twirling two equilateral triangular spinners labelled 1 , 2 and 3 and X, Y and Z

d drawing two tickets from a hat containing a number of pink, blue and white tickets.

e drawing two beads from a bag containing 3 red and 4 blue beads.

4 Draw a Venn diagram to show a class of 20 students where 10 study History, 15 study Geography, and

2 study neither subject.

From the methods of showing sample spaces in the previous section, we can find the probabilities of combined

events.

These are theoretical probabilities which are calculated using

P(event happens)=

number of ways the event can happen

total number of possible outcomes

:

Example 7 Self Tutor

Three coins are tossed. Write down a list of all possible outcomes.

Find the probability of getting:

a 3 heads b at least one head

c 3 heads if it is known that there is at least one head.

The sample space is: HHH HHT TTH TTT

HTH THT

THH HTT

a P( 3 heads)=^18

b P(at least one H)=^78 fall except TTTg

c P(HHH knowing at least one H)=^17

fThe sample space now excludes TTTg

F THEORETICAL PROBABILITY [10.4, 10.6]

Notice how we list

the outcomes in a

systematic way.

Probability (Chapter 25) 515

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Y:\HAESE\IGCSE01\IG01_25\515IGCSE01_25.CDR Monday, 27 October 2008 2:31:01 PM PETER